My earlier advice still stands. Seems that you've decided against it, which is fine, it's your trip! I just think it is wildly inefficient to go all the way to Mt Cook, then back to Queenstown, then drive to CHC. And why not overnight in Wanaka on arrival to break up the long, long drive from Queenstown to Frans Josef? The whole trip sounds absolutely exhausting. Hopefully your adrenaline will keep you going for those 12 days!
As for other things to do in Queenstown, you've pretty much packed the rest of your trip full besides those two 1/2 days. I'd leave that time to do something spontaneous or relaxing in Queenstown. You won't lack options.
Enjoy NZ.